Do not assign exactly the same meaning to the two verbs in a contest expression:
PartVerbFunction
ContestخَاصَمَنِيDisputed with me
OutcomeفَخَصَمْتُهُI prevailed over him
The connective فَـ indicates sequence; it does not itself create the sense of victory. The relevant morphological point is the form selected to express the successful outcome. The wider context remains important.